International System of Units (SI)

Metrology Measurement standards SI units Science

International System of Units (SI): Modern Metric System of Measurement

Introduction

The International System of Units (SI) is the globally accepted system for all measurements, forming the backbone of science, engineering, industry, and daily commerce. Established and maintained by the Bureau International des Poids et Mesures (BIPM), SI is built on seven rigorously defined base units and a comprehensive framework of derived units and prefixes. This system ensures that measurements are consistent, precise, and universally understandable—from laboratories and hospitals to factories and airports.

Key Concepts and Terminology

  • SI (International System of Units): The world’s single, coherent measurement system, encompassing base units, derived units, and prefixes.
  • Metric System: The historical foundation of SI, based on decimal units and introduced in France in the late 18th century.
  • Base Unit: One of the seven fundamental units defined in SI, each based on a specific dimension of measurement.
  • Derived Unit: Units formed by algebraic combinations of base units, representing additional physical quantities.
  • Prefix: Standardized modifiers to scale units by powers of ten, making SI adaptable for any magnitude.
  • Defining Constant: A fundamental constant of nature used to define SI base units, ensuring permanence and universality.
  • CGPM: The international authority (General Conference on Weights and Measures) overseeing SI.
  • BIPM: The international organization (Bureau International des Poids et Mesures) responsible for maintaining and disseminating SI.
  • NIST: The US agency (National Institute of Standards and Technology) in charge of SI implementation in the United States.

Historical Development

From the Metric Revolution to SI

France’s late 18th-century metric revolution aimed to simplify and standardize measurement via the meter and kilogram, defined by natural phenomena and the decimal system. The Meter Convention of 1875 created the BIPM and established an international measurement framework, later overseen by the CGPM.

Key Milestones

  • 1960: SI formally adopted by the 11th CGPM, consolidating earlier metric systems.
  • 1983: The meter redefined by the speed of light in vacuum.
  • 2019: The kilogram, ampere, kelvin, and mole were redefined using fundamental constants (Planck constant, elementary charge, Boltzmann constant, Avogadro constant).

This evolution reflects a drive for ever-greater precision, accessibility, and universality. Today, SI definitions are entirely decoupled from physical artifacts and instead anchored in immutable constants of nature.

SI Structure and Architecture

The architecture of SI is logical, hierarchical, and coherent:

  • Seven Base Units: Each for a unique dimension of measurement.
  • Derived Units: Formed by combining base units, expressing a wide array of physical quantities.
  • Prefixes: Scale units for extremely large or small quantities.
  • Coherence: Derived units are direct products or quotients of base units, requiring no conversion factors.
  • Supplementary Units: Radian and steradian, for plane and solid angles.

Any measurable quantity can be described within SI, ensuring transparency and consistency across all scientific and technical disciplines.

The Seven SI Base Units

Physical QuantityUnit NameSymbolDefinition (2019+)Defining Constant(s)
LengthmetermThe distance light travels in vacuum in 1/299,792,458 seconds.Speed of light, c
MasskilogramkgDefined by fixing the Planck constant h to 6.62607015 × 10⁻³⁴ J·s.Planck constant, h
TimesecondsDuration of 9,192,631,770 periods of the cesium-133 atom’s hyperfine transition.Cs-133 transition frequency, Δν_Cs
Electric currentampereADefined by fixing the elementary charge e to 1.602176634 × 10⁻¹⁹ C.Elementary charge, e
Thermodynamic temperaturekelvinKDefined by fixing the Boltzmann constant k to 1.380649 × 10⁻²³ J/K.Boltzmann constant, k
Amount of substancemolemolContains 6.02214076 × 10²³ specified elementary entities (Avogadro constant).Avogadro constant, Nₐ
Luminous intensitycandelacdDefined by fixing the luminous efficacy K_cd of monochromatic radiation (540 × 10¹² Hz) to 683 lm/W.Luminous efficacy, K_cd

Applications

  • Meter (m): Used for measuring all lengths and distances—critical in construction, navigation, and science.
  • Kilogram (kg): The standard for mass in trade, science, and industry.
  • Second (s): The universal time unit, foundational for timekeeping and synchronization.
  • Ampere (A): For all electrical current measurements.
  • Kelvin (K): The thermodynamic temperature unit for science and technology.
  • Mole (mol): Central in chemistry, linking atomic/molecular scale to bulk quantities.
  • Candela (cd): For measuring luminous intensity, crucial in lighting design and safety.

SI Derived Units

Derived units are algebraic combinations of base units, reflecting how physical quantities relate to each other.

QuantityUnit NameSymbolBase Unit Expression
Areasquare meterm × m
Volumecubic meterm × m × m
Speedmeter per secondm/sm / s
Accelerationmeter per second squaredm/s²m / s²
Densitykilogram per cubic meterkg/m³kg / m³
Concentrationmole per cubic metermol/m³mol / m³
Luminancecandela per square metercd/m²cd / m²
Magnetic field strengthampere per meterA/mA / m

Special Names and Symbols

Many commonly used derived units have unique names and symbols:

QuantityUnit NameSymbolBase Unit Expression
ForcenewtonNkg·m/s²
PressurepascalPakg/(m·s²)
EnergyjouleJkg·m²/s²
PowerwattWkg·m²/s³
Electric chargecoulombCA·s
VoltagevoltVkg·m²/(s³·A)
ResistanceohmΩkg·m²/(s³·A²)
ConductancesiemensSs³·A²/(kg·m²)
CapacitancefaradFs⁴·A²/(kg·m²)
Magnetic fluxweberWbkg·m²/(s²·A)
Magnetic flux densityteslaTkg/(s²·A)
InductancehenryHkg·m²/(s²·A²)
Luminous fluxlumenlmcd·sr
Illuminanceluxlxcd·sr/m²
RadioactivitybecquerelBqs⁻¹
Absorbed dosegrayGym²/s²
Dose equivalentsievertSvm²/s²
Catalytic activitykatalkatmol/s

Real-World Examples

  • Newton (N): For force, e.g., thrust in aircraft engines.
  • Joule (J): For energy, e.g., fuel energy content.
  • Pascal (Pa): For pressure, e.g., atmospheric or hydraulic pressure.

SI Prefixes

SI prefixes make it easy to express very large or small quantities by scaling units in powers of ten.

FactorPrefixSymbolFactorPrefixSymbol
10¹⁸exaE10⁻¹decid
10¹⁵petaP10⁻²centic
10¹²teraT10⁻³millim
10⁹gigaG10⁻⁶microμ
10⁶megaM10⁻⁹nanon
10³kilok10⁻¹²picop
10²hectoh10⁻¹⁵femtof
10¹dekada10⁻¹⁸attoa

Application

  • 1 kilometer (km) = 1,000 meters
  • 1 milligram (mg) = 0.001 grams
  • 1 gigahertz (GHz) = 1,000,000,000 Hz

Prefixes accommodate measurement in everything from nanotechnology to astronomy.

SI Supplementary Units: Angles

  • Radian (rad): The SI unit for plane angle, used in mathematics and physics.
  • Steradian (sr): The SI unit for solid angle, important in optics and radiometry.

Though dimensionless, these units clarify context in formulas and calculations involving angles, rotational kinematics, and radiance.

Non-SI Units Accepted with SI

Some non-SI units are officially sanctioned for use with SI due to their widespread practical importance:

QuantityUnit NameSymbolSI Relationship
Timeminutemin1 min = 60 s
hourh1 h = 60 min = 3,600 s
dayd1 d = 24 h = 86,400 s
Angledegree°1° = (π/180) rad
minute1′ = (1/60)°
second1″ = (1/60)′
VolumeliterL, l1 L = 0.001 m³
Massmetric tont1 t = 1,000 kg
  • Practical examples: Minutes and hours (timekeeping), degrees (navigation), liters (fuel, beverages), metric tons (shipping).

SI Usage: Standards and Best Practices

  • Symbols: Use capital letter for unit symbols named after individuals (e.g., N for newton, Pa for pascal).
  • Spacing: Leave a space between the number and unit symbol (e.g., 25 kg, not 25kg).
  • Decimal marker: Use either a point or comma (e.g., 3.14 or 3,14), but be consistent.
  • Pluralization: SI unit symbols do not take a plural form (e.g., 5 km, not 5 kms).
  • Prefixes: Only one prefix per unit (e.g., not mkm for micrometer, but μm).

Global Governance and Adoption

  • International: The BIPM (France) maintains the SI and publishes the SI Brochure. The CGPM (member states) approves changes.
  • National: Institutes like NIST (USA), PTB (Germany), and NPL (UK) implement and disseminate SI nationally.
  • Legal and Commercial: SI is mandated or recommended in nearly all countries for trade, regulation, and education.

SI in Science, Industry, and Everyday Life

  • Science and Engineering: SI underpins all scientific research, enabling global collaboration and reproducibility.
  • Industry: Ensures interoperability in manufacturing, quality assurance, and international trade.
  • Daily life: Used in medicine, construction, navigation, weather reporting, and consumer products.

Conclusion

The International System of Units (SI) is the essential foundation for all precise and consistent measurement worldwide. Its structure—anchored in natural constants and universal principles—ensures that every measurement, whether in a laboratory, factory, or daily transaction, is meaningful and comparable anywhere on Earth. SI’s ongoing evolution, responsiveness to scientific advances, and unwavering commitment to clarity make it indispensable for progress across all domains.

Further Resources

See Also

Frequently Asked Questions

What is the difference between SI and the metric system?
SI is the modern, internationally agreed version of the metric system, with precise definitions and a broader set of units and prefixes.

How often are SI units redefined?
SI units are only redefined when advances in science and technology necessitate more stable, precise definitions—such as the 2019 redefinitions based on fundamental constants.

Can SI be used everywhere?
Yes, SI is universal and mandated or recommended by nearly all nations for official use in science, engineering, trade, and education.

Where do I find the latest SI definitions?
The official source is the BIPM SI Brochure , regularly updated with all definitions, recommendations, and usage guidance.

Frequently Asked Questions

Why is the International System of Units (SI) important?

SI provides a universal measurement language, allowing scientists, engineers, and industries worldwide to communicate results, share data, and collaborate without confusion. Its precise definitions, based on physical constants, offer unparalleled accuracy and reproducibility.

What are the seven SI base units?

The seven SI base units are: meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.

How are SI units redefined?

SI units are redefined by the CGPM using fundamental physical constants, such as the speed of light or Planck constant, making the units stable, universally accessible, and independent of physical artifacts.

Are non-SI units ever used with SI?

Yes, some non-SI units like minute, hour, day, degree (°), liter (L), and metric ton (t) are officially accepted for use with SI when their relationships to SI units are precisely defined.

Who maintains the SI system?

The Bureau International des Poids et Mesures (BIPM) maintains the SI, with oversight and updates determined by the General Conference on Weights and Measures (CGPM). National agencies, such as NIST in the USA, implement SI locally.

Standardize Your Measurements with SI

Adopting the International System of Units (SI) enables accurate, reliable, and globally recognized measurements—essential for science, engineering, and commerce.

Learn more

SI Unit

SI Unit

The International System of Units (SI) is the universal metric system underpinning all scientific, engineering, and aviation measurement standards. SI ensures p...

7 min read
Aviation Aerospace +3
Unit

Unit

A unit is a defined quantity used as a standard for measuring physical quantities. Standard units, such as those in the SI system, ensure consistency, safety, a...

6 min read
Measurement Standard Unit +3
Uncertainty – Estimated Range of Measurement Error – Measurement

Uncertainty – Estimated Range of Measurement Error – Measurement

Uncertainty in measurement defines the estimated range within which the true value of a quantity lies, accounting for all known sources of error. Proper uncerta...

7 min read
Measurement Aviation +3